Bases in Diagrammatic Quantum Protocols

被引:13
作者
Coecke, Bob [1 ]
Perdrix, Simon [1 ]
Paquette, Eric Oliver [2 ]
机构
[1] Univ Oxford, Comp Lab, Wolfson Bldg,Pks Rd, Oxford OX1 3QD, England
[2] Univ Montreal, Dept Informat & Rech Operat, LITQ, Montreal, PQ H3C 3J7, Canada
基金
英国工程与自然科学研究理事会;
关键词
categorical semantics; quantum protocols; diagrammatic calculus; abstract bases;
D O I
10.1016/j.entcs.2008.10.009
中图分类号
TP301 [理论、方法];
学科分类号
081202 ;
摘要
This paper contains two new results: (i) We amend the notion of abstract basis in a dagger symmetric monoidal category, as well as its corresponding graphical representation, in order to accommodate non-self-dual dagger compact structures; this is crucial for obtaining a planar diagrammatical representation of the induced dagger compact structure as well as for representing many complementary bases within one diagrammatic calculus. (ii) We (crucially) rely on these basis structures in a purely diagrammatic derivation of the quantum state transfer protocol; this derivation provides interesting insights in the distinct structural resources required for state-transfer and teleportation as models of quantum computing.
引用
收藏
页码:131 / 152
页数:22
相关论文
共 22 条
  • [1] A categorical semantics of quantum protocols
    Abramsky, S
    Coecke, B
    [J]. 19TH ANNUAL IEEE SYMPOSIUM ON LOGIC IN COMPUTER SCIENCE, PROCEEDINGS, 2004, : 415 - 425
  • [2] TELEPORTING AN UNKNOWN QUANTUM STATE VIA DUAL CLASSICAL AND EINSTEIN-PODOLSKY-ROSEN CHANNELS
    BENNETT, CH
    BRASSARD, G
    CREPEAU, C
    JOZSA, R
    PERES, A
    WOOTTERS, WK
    [J]. PHYSICAL REVIEW LETTERS, 1993, 70 (13) : 1895 - 1899
  • [3] CARTESIAN BICATEGORIES .1.
    CARBONI, A
    WALTERS, RFC
    [J]. JOURNAL OF PURE AND APPLIED ALGEBRA, 1987, 49 (1-2) : 11 - 32
  • [4] Coecke B., 2007, CRC APPL MATH NONLIN, P567
  • [5] COECKE B, 2008, RR0803 OXF U COMP LA
  • [6] Coecke B., 2008, CLASSICAL Q IN PRESS
  • [7] Coecke B., 2008, LECT NOTES IN PRESS
  • [8] Coecke B., 2006, P QUANT PROGR LANG
  • [9] De-linearizing Linearity: Projective Quantum Axiomatics From Strong Compact Closure
    Coecke, Bob
    [J]. ELECTRONIC NOTES IN THEORETICAL COMPUTER SCIENCE, 2007, 170 : 49 - 72
  • [10] Fuchs E, 2002, NUCL PHYS B, V646, P353, DOI 10.1016/S0550-3213(02)00744-7